12a
0632
(K12a
0632
)
A knot diagram
1
Linearized knot diagam
3 7 10 9 11 2 6 12 4 1 8 5
Solving Sequence
3,10 4,7
2 1 11 6 9 5 12 8
c
3
c
2
c
1
c
10
c
6
c
9
c
4
c
12
c
8
c
5
, c
7
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h4.99554 × 10
194
u
93
+ 1.87631 × 10
195
u
92
+ ··· + 1.61849 × 10
196
b − 2.06106 × 10
197
,
3.26120 × 10
197
u
93
− 1.40330 × 10
198
u
92
+ ··· + 3.28554 × 10
198
a + 8.49179 × 10
199
,
u
94
− u
93
+ ··· − 167u − 29i
I
u
2
= h−u
12
− 7u
10
− 17u
8
− u
7
− 15u
6
− 4u
5
− u
4
− 4u
3
+ u
2
+ b − 1,
u
15
+ 9u
13
+ 31u
11
+ 49u
9
+ 32u
7
+ 5u
5
+ 3u
3
+ a + 2u, u
20
+ 12u
18
+ ··· + 2u − 1i
* 2 irreducible components of dim
C
= 0, with total 114 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= h5.00 × 10
194
u
93
+ 1.88 × 10
195
u
92
+ · · · + 1.62 × 10
196
b − 2.06 ×
10
197
, 3.26 × 10
197
u
93
− 1.40 × 10
198
u
92
+ · · · + 3.29 × 10
198
a + 8.49 ×
10
199
, u
94
− u
93
+ · · · − 167u − 29i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
−0.0992592u
93
+ 0.427114u
92
+ ··· − 146.954u − 25.8459
−0.0308654u
93
− 0.115930u
92
+ ··· + 68.0928u + 12.7344
a
2
=
−0.538405u
93
+ 0.447589u
92
+ ··· + 266.311u + 35.3348
0.293053u
93
− 0.414594u
92
+ ··· − 26.7401u + 0.924989
a
1
=
−0.245351u
93
+ 0.0329949u
92
+ ··· + 239.571u + 36.2598
0.293053u
93
− 0.414594u
92
+ ··· − 26.7401u + 0.924989
a
11
=
−0.335863u
93
+ 0.0931342u
92
+ ··· + 376.355u + 59.6146
0.173090u
93
− 0.229501u
92
+ ··· − 103.638u − 13.5395
a
6
=
−0.973604u
93
+ 1.46961u
92
+ ··· − 64.1810u − 31.6883
−0.0839155u
93
− 0.212165u
92
+ ··· + 128.396u + 23.5613
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
−0.300038u
93
+ 0.154180u
92
+ ··· + 196.014u + 27.6672
0.296675u
93
− 0.441920u
92
+ ··· + 7.50288u + 7.58897
a
8
=
−0.389629u
93
− 0.0751627u
92
+ ··· + 300.697u + 46.4877
−0.0198539u
93
+ 0.200468u
92
+ ··· − 84.1348u − 15.6577
(ii) Obstruction class = −1
(iii) Cusp Shapes = −1.16644u
93
+ 1.34986u
92
+ ··· + 102.241u − 6.06992
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
7
u
94
+ 27u
93
+ ··· + 38u + 1
c
2
, c
6
u
94
− u
93
+ ··· − 6u − 1
c
3
, c
4
, c
9
u
94
+ u
93
+ ··· + 167u − 29
c
5
u
94
+ u
93
+ ··· − 48236u − 34973
c
8
, c
11
u
94
+ u
93
+ ··· + 18u − 1
c
10
u
94
− 15u
93
+ ··· − 23727557u + 1575181
c
12
u
94
− 4u
93
+ ··· − 1684565u + 327443
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
94
+ 89y
93
+ ··· + 330y + 1
c
2
, c
6
y
94
− 27y
93
+ ··· − 38y + 1
c
3
, c
4
, c
9
y
94
+ 105y
93
+ ··· + 13233y + 841
c
5
y
94
− 39y
93
+ ··· − 42017779234y + 1223110729
c
8
, c
11
y
94
− 87y
93
+ ··· − 396y + 1
c
10
y
94
+ 49y
93
+ ··· − 1793204056987y + 2481195182761
c
12
y
94
− 46y
93
+ ··· − 4312336575555y + 107218918249
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.820738 + 0.587626I
a = 0.440823 − 0.310456I
b = 0.881355 − 0.271423I
0.96039 + 2.29358I 0
u = 0.820738 − 0.587626I
a = 0.440823 + 0.310456I
b = 0.881355 + 0.271423I
0.96039 − 2.29358I 0
u = 0.718782 + 0.561750I
a = −0.919278 + 0.814379I
b = −1.040590 − 0.339974I
1.04618 − 7.42407I 0
u = 0.718782 − 0.561750I
a = −0.919278 − 0.814379I
b = −1.040590 + 0.339974I
1.04618 + 7.42407I 0
u = 0.199350 + 0.836635I
a = 0.26123 + 1.52112I
b = −0.781807 − 0.449145I
1.25072 − 1.88705I 0
u = 0.199350 − 0.836635I
a = 0.26123 − 1.52112I
b = −0.781807 + 0.449145I
1.25072 + 1.88705I 0
u = −0.815773 + 0.799685I
a = −0.606742 − 0.612269I
b = 0.790217 + 0.879227I
9.05964 + 6.09171I 0
u = −0.815773 − 0.799685I
a = −0.606742 + 0.612269I
b = 0.790217 − 0.879227I
9.05964 − 6.09171I 0
u = −0.271517 + 0.804423I
a = 0.623640 + 1.187280I
b = 0.738176 + 0.114073I
−1.40142 − 0.50343I 0
u = −0.271517 − 0.804423I
a = 0.623640 − 1.187280I
b = 0.738176 − 0.114073I
−1.40142 + 0.50343I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.635589 + 0.559738I
a = 0.107171 + 0.363611I
b = −0.877502 − 0.782060I
3.53268 − 2.95131I 0
u = −0.635589 − 0.559738I
a = 0.107171 − 0.363611I
b = −0.877502 + 0.782060I
3.53268 + 2.95131I 0
u = 0.865061 + 0.767344I
a = 0.51007 − 1.61748I
b = 0.995348 + 0.801095I
8.4200 − 12.3261I 0
u = 0.865061 − 0.767344I
a = 0.51007 + 1.61748I
b = 0.995348 − 0.801095I
8.4200 + 12.3261I 0
u = −0.077414 + 1.155390I
a = 0.72139 − 2.10591I
b = −0.832174 + 0.633495I
1.26169 + 2.45313I 0
u = −0.077414 − 1.155390I
a = 0.72139 + 2.10591I
b = −0.832174 − 0.633495I
1.26169 − 2.45313I 0
u = 0.663089 + 0.467881I
a = −0.682449 + 1.189480I
b = −0.897129 − 0.774236I
3.46999 − 2.91507I 0
u = 0.663089 − 0.467881I
a = −0.682449 − 1.189480I
b = −0.897129 + 0.774236I
3.46999 + 2.91507I 0
u = −0.510396 + 0.617981I
a = −0.006012 + 0.574248I
b = −0.084323 − 0.749330I
4.13181 + 3.70371I 0
u = −0.510396 − 0.617981I
a = −0.006012 − 0.574248I
b = −0.084323 + 0.749330I
4.13181 − 3.70371I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.586789 + 0.543439I
a = −0.761137 − 0.077902I
b = 0.824788 − 0.804257I
3.76120 − 1.30617I 0
u = 0.586789 − 0.543439I
a = −0.761137 + 0.077902I
b = 0.824788 + 0.804257I
3.76120 + 1.30617I 0
u = −0.620759 + 0.498143I
a = 1.23807 + 1.75646I
b = 0.943160 − 0.775930I
3.39908 + 7.24288I 0
u = −0.620759 − 0.498143I
a = 1.23807 − 1.75646I
b = 0.943160 + 0.775930I
3.39908 − 7.24288I 0
u = −1.150250 + 0.461742I
a = −0.335761 − 1.188530I
b = −0.844510 + 0.830835I
7.74170 + 0.30120I 0
u = −1.150250 − 0.461742I
a = −0.335761 + 1.188530I
b = −0.844510 − 0.830835I
7.74170 − 0.30120I 0
u = 1.142230 + 0.528154I
a = 0.104805 − 0.704670I
b = −0.942928 + 0.799373I
7.43573 + 5.79082I 0
u = 1.142230 − 0.528154I
a = 0.104805 + 0.704670I
b = −0.942928 − 0.799373I
7.43573 − 5.79082I 0
u = −0.691704 + 0.069857I
a = 1.73090 + 0.13000I
b = 0.185748 − 0.106850I
2.85068 − 0.00394I 4.77299 + 0.I
u = −0.691704 − 0.069857I
a = 1.73090 − 0.13000I
b = 0.185748 + 0.106850I
2.85068 + 0.00394I 4.77299 + 0.I
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.295863 + 0.613012I
a = 0.73322 + 1.80671I
b = −0.809513 − 0.268723I
1.13533 − 2.03881I 0. + 6.81649I
u = 0.295863 − 0.613012I
a = 0.73322 − 1.80671I
b = −0.809513 + 0.268723I
1.13533 + 2.03881I 0. − 6.81649I
u = −0.482695 + 0.333452I
a = −2.16015 − 0.87654I
b = −0.914998 + 0.229995I
−2.63624 + 3.34700I −9.84874 − 7.94099I
u = −0.482695 − 0.333452I
a = −2.16015 + 0.87654I
b = −0.914998 − 0.229995I
−2.63624 − 3.34700I −9.84874 + 7.94099I
u = −0.000183 + 0.585754I
a = 0.952288 − 0.418442I
b = −0.755983 + 0.900316I
7.97844 + 0.55523I 6.56904 − 0.52995I
u = −0.000183 − 0.585754I
a = 0.952288 + 0.418442I
b = −0.755983 − 0.900316I
7.97844 − 0.55523I 6.56904 + 0.52995I
u = 0.01950 + 1.42476I
a = −0.332704 + 0.558349I
b = −1.049140 − 0.266255I
3.04541 − 0.96461I 0
u = 0.01950 − 1.42476I
a = −0.332704 − 0.558349I
b = −1.049140 + 0.266255I
3.04541 + 0.96461I 0
u = −0.07864 + 1.45458I
a = 0.64180 − 1.99812I
b = 0.733749 + 0.278862I
8.05807 + 1.16577I 0
u = −0.07864 − 1.45458I
a = 0.64180 + 1.99812I
b = 0.733749 − 0.278862I
8.05807 − 1.16577I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.11659 + 1.46166I
a = 0.574879 + 1.242790I
b = 1.012810 − 0.292217I
3.23851 + 5.39050I 0
u = −0.11659 − 1.46166I
a = 0.574879 − 1.242790I
b = 1.012810 + 0.292217I
3.23851 − 5.39050I 0
u = 0.300332 + 0.436318I
a = 0.436112 + 0.068253I
b = 0.002092 + 0.379935I
−0.137046 − 1.130850I −2.15439 + 5.92996I
u = 0.300332 − 0.436318I
a = 0.436112 − 0.068253I
b = 0.002092 − 0.379935I
−0.137046 + 1.130850I −2.15439 − 5.92996I
u = −0.051296 + 0.521935I
a = −2.87878 − 1.09502I
b = 0.931068 + 0.788334I
7.18856 − 5.21612I 6.82948 + 5.47677I
u = −0.051296 − 0.521935I
a = −2.87878 + 1.09502I
b = 0.931068 − 0.788334I
7.18856 + 5.21612I 6.82948 − 5.47677I
u = −0.085886 + 0.513350I
a = −0.74177 − 2.07353I
b = −1.021080 + 0.802754I
7.16169 + 5.74033I 4.97732 − 6.13962I
u = −0.085886 − 0.513350I
a = −0.74177 + 2.07353I
b = −1.021080 − 0.802754I
7.16169 − 5.74033I 4.97732 + 6.13962I
u = 0.378489 + 0.334490I
a = 0.711457 + 0.594518I
b = 1.135660 − 0.192281I
0.066201 − 0.543447I −1.68971 + 10.03219I
u = 0.378489 − 0.334490I
a = 0.711457 − 0.594518I
b = 1.135660 + 0.192281I
0.066201 + 0.543447I −1.68971 − 10.03219I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.04902 + 1.50808I
a = −0.205130 + 0.843593I
b = 0.004830 − 0.661595I
6.35559 − 2.20338I 0
u = 0.04902 − 1.50808I
a = −0.205130 − 0.843593I
b = 0.004830 + 0.661595I
6.35559 + 2.20338I 0
u = 0.09006 + 1.50644I
a = 0.177929 − 0.400798I
b = −1.312220 + 0.208394I
6.32186 − 2.06708I 0
u = 0.09006 − 1.50644I
a = 0.177929 + 0.400798I
b = −1.312220 − 0.208394I
6.32186 + 2.06708I 0
u = −0.28507 + 1.50115I
a = −0.925190 − 0.903580I
b = −0.729288 + 0.331136I
8.32963 + 4.12866I 0
u = −0.28507 − 1.50115I
a = −0.925190 + 0.903580I
b = −0.729288 − 0.331136I
8.32963 − 4.12866I 0
u = −0.17857 + 1.52580I
a = −0.19993 − 2.38320I
b = −0.981214 + 0.788797I
10.0840 + 10.0843I 0
u = −0.17857 − 1.52580I
a = −0.19993 + 2.38320I
b = −0.981214 − 0.788797I
10.0840 − 10.0843I 0
u = 0.01876 + 1.53818I
a = 0.50168 + 2.75318I
b = −0.906877 − 0.816322I
14.2850 − 1.0715I 0
u = 0.01876 − 1.53818I
a = 0.50168 − 2.75318I
b = −0.906877 + 0.816322I
14.2850 + 1.0715I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.16297 + 1.53875I
a = 1.35628 − 0.85930I
b = −0.793481 + 0.850541I
10.66380 − 3.97201I 0
u = 0.16297 − 1.53875I
a = 1.35628 + 0.85930I
b = −0.793481 − 0.850541I
10.66380 + 3.97201I 0
u = 0.056940 + 0.447762I
a = 0.07733 − 4.59205I
b = 0.848197 + 0.813608I
7.44639 − 0.78804I 7.86918 − 0.12351I
u = 0.056940 − 0.447762I
a = 0.07733 + 4.59205I
b = 0.848197 − 0.813608I
7.44639 + 0.78804I 7.86918 + 0.12351I
u = −0.02446 + 1.55322I
a = −0.37266 + 1.86761I
b = 1.087400 − 0.843941I
14.2681 + 6.1381I 0
u = −0.02446 − 1.55322I
a = −0.37266 − 1.86761I
b = 1.087400 + 0.843941I
14.2681 − 6.1381I 0
u = 0.20649 + 1.53975I
a = −0.15588 − 1.89554I
b = 0.994097 + 0.801925I
10.13680 − 6.11038I 0
u = 0.20649 − 1.53975I
a = −0.15588 + 1.89554I
b = 0.994097 − 0.801925I
10.13680 + 6.11038I 0
u = −0.00658 + 1.55610I
a = 1.70159 + 1.60544I
b = −0.888262 − 0.822282I
14.3430 − 5.0485I 0
u = −0.00658 − 1.55610I
a = 1.70159 − 1.60544I
b = −0.888262 + 0.822282I
14.3430 + 5.0485I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21724 + 1.54298I
a = 0.111391 − 1.183470I
b = 1.142230 + 0.409534I
7.96596 − 10.79960I 0
u = 0.21724 − 1.54298I
a = 0.111391 + 1.183470I
b = 1.142230 − 0.409534I
7.96596 + 10.79960I 0
u = 0.08889 + 1.55890I
a = −1.06467 − 1.11922I
b = 0.633541 + 0.264130I
8.41592 − 3.43999I 0
u = 0.08889 − 1.55890I
a = −1.06467 + 1.11922I
b = 0.633541 − 0.264130I
8.41592 + 3.43999I 0
u = 0.435116
a = 1.19176
b = 0.785407
−1.15748 −8.95110
u = −0.00748 + 1.56799I
a = −0.84679 + 1.38761I
b = 0.737098 − 1.016210I
15.3759 + 0.6273I 0
u = −0.00748 − 1.56799I
a = −0.84679 − 1.38761I
b = 0.737098 + 1.016210I
15.3759 − 0.6273I 0
u = −0.14946 + 1.56329I
a = −0.237754 − 1.199410I
b = 0.126842 + 0.945947I
11.42390 + 6.11641I 0
u = −0.14946 − 1.56329I
a = −0.237754 + 1.199410I
b = 0.126842 − 0.945947I
11.42390 − 6.11641I 0
u = −0.15739 + 1.56991I
a = −0.87556 − 1.20713I
b = 0.791167 + 0.873078I
10.76480 − 0.11126I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.15739 − 1.56991I
a = −0.87556 + 1.20713I
b = 0.791167 − 0.873078I
10.76480 + 0.11126I 0
u = 0.18660 + 1.62275I
a = 0.301803 − 0.266790I
b = −0.627194 + 0.322697I
8.67469 − 1.47071I 0
u = 0.18660 − 1.62275I
a = 0.301803 + 0.266790I
b = −0.627194 − 0.322697I
8.67469 + 1.47071I 0
u = −0.24840 + 1.63617I
a = 1.08887 + 1.12188I
b = −0.782845 − 0.940726I
17.1334 + 10.0750I 0
u = −0.24840 − 1.63617I
a = 1.08887 − 1.12188I
b = −0.782845 + 0.940726I
17.1334 − 10.0750I 0
u = 0.27031 + 1.63345I
a = 0.04427 + 2.10192I
b = −1.030210 − 0.824005I
16.3449 − 16.5646I 0
u = 0.27031 − 1.63345I
a = 0.04427 − 2.10192I
b = −1.030210 + 0.824005I
16.3449 + 16.5646I 0
u = −0.289565
a = 6.60678
b = −0.406278
2.74746 8.96970
u = −0.234229 + 0.135956I
a = 3.16603 − 0.77183I
b = 0.872341 + 0.394830I
−1.88761 − 1.44450I −11.71074 + 3.98998I
u = −0.234229 − 0.135956I
a = 3.16603 + 0.77183I
b = 0.872341 − 0.394830I
−1.88761 + 1.44450I −11.71074 − 3.98998I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.38422 + 1.68637I
a = −0.06395 + 1.90894I
b = 0.909420 − 0.826421I
14.9021 + 6.2030I 0
u = −0.38422 − 1.68637I
a = −0.06395 − 1.90894I
b = 0.909420 + 0.826421I
14.9021 − 6.2030I 0
u = 0.35426 + 1.70934I
a = −0.87648 + 1.13190I
b = 0.892376 − 0.832193I
14.9552 − 0.0207I 0
u = 0.35426 − 1.70934I
a = −0.87648 − 1.13190I
b = 0.892376 + 0.832193I
14.9552 + 0.0207I 0
14
II.
I
u
2
= h−u
12
−7u
10
+· · ·+b−1, u
15
+9u
13
+· · ·+a+2u, u
20
+12u
18
+· · ·+2u−1i
(i) Arc colorings
a
3
=
1
0
a
10
=
0
u
a
4
=
1
u
2
a
7
=
−u
15
− 9u
13
− 31u
11
− 49u
9
− 32u
7
− 5u
5
− 3u
3
− 2u
u
12
+ 7u
10
+ 17u
8
+ u
7
+ 15u
6
+ 4u
5
+ u
4
+ 4u
3
− u
2
+ 1
a
2
=
u
19
+ 11u
17
+ ··· + 2u + 1
−u
19
− 11u
17
+ ··· − 4u
3
− 1
a
1
=
u
3
+ 2u
−u
19
− 11u
17
+ ··· − 4u
3
− 1
a
11
=
−u
7
− 4u
5
− 4u
3
−u
9
− 5u
7
− 7u
5
− u
3
+ 2u
a
6
=
u
10
+ 6u
8
+ 12u
6
+ 8u
4
+ u
2
+ 1
u
12
+ 7u
10
+ 17u
8
+ 15u
6
+ u
4
− 2u
2
a
9
=
u
u
3
+ u
a
5
=
u
2
+ 1
u
4
+ 2u
2
a
12
=
u
19
+ 11u
17
+ ··· + 3u + 1
−u
19
− 11u
17
+ ··· + u − 1
a
8
=
−u
17
− 10u
15
+ ··· − 3u − 1
u
17
+ 10u
15
+ ··· + u + 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 4u
19
+ 47u
17
− 2u
16
+ 225u
15
− 16u
14
+ 553u
13
− 42u
12
+
709u
11
− 24u
10
+ 398u
9
+ 59u
8
+ 23u
7
+ 72u
6
+ u
4
+ 36u
3
− 5u
2
+ 2u + 1
15
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
20
− 8u
19
+ ··· − 15u + 1
c
2
u
20
− 4u
18
+ ··· + u + 1
c
3
, c
4
u
20
+ 12u
18
+ ··· + 2u − 1
c
5
u
20
− 2u
18
+ ··· − u − 1
c
6
u
20
− 4u
18
+ ··· − u + 1
c
7
u
20
+ 8u
19
+ ··· + 15u + 1
c
8
u
20
− 4u
19
+ ··· + 5u + 1
c
9
u
20
+ 12u
18
+ ··· − 2u − 1
c
10
u
20
+ 4u
19
+ ··· + 6u + 1
c
11
u
20
+ 4u
19
+ ··· − 5u + 1
c
12
u
20
+ u
19
+ ··· + 2u
2
− 1
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
20
+ 16y
19
+ ··· − 19y + 1
c
2
, c
6
y
20
− 8y
19
+ ··· − 15y + 1
c
3
, c
4
, c
9
y
20
+ 24y
19
+ ··· − 8y + 1
c
5
y
20
− 4y
19
+ ··· − 7y + 1
c
8
, c
11
y
20
− 24y
19
+ ··· + 39y + 1
c
10
y
20
+ 4y
19
+ ··· − 20y + 1
c
12
y
20
− 7y
19
+ ··· − 4y + 1
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.082617 + 0.972592I
a = 0.46585 + 2.01695I
b = −0.820647 − 0.519052I
0.07220 − 2.08153I −5.27988 + 3.56850I
u = 0.082617 − 0.972592I
a = 0.46585 − 2.01695I
b = −0.820647 + 0.519052I
0.07220 + 2.08153I −5.27988 − 3.56850I
u = 0.145657 + 0.667229I
a = 0.668097 − 0.491145I
b = 0.787890 − 0.308801I
−0.99868 + 1.31531I −1.48801 − 4.97789I
u = 0.145657 − 0.667229I
a = 0.668097 + 0.491145I
b = 0.787890 + 0.308801I
−0.99868 − 1.31531I −1.48801 + 4.97789I
u = −0.596499 + 0.244913I
a = −1.02878 − 1.75372I
b = −0.826291 + 0.815126I
6.42751 + 1.06605I −1.05015 − 2.88825I
u = −0.596499 − 0.244913I
a = −1.02878 + 1.75372I
b = −0.826291 − 0.815126I
6.42751 − 1.06605I −1.05015 + 2.88825I
u = 0.563183 + 0.309037I
a = 0.586211 − 0.158353I
b = −0.951603 + 0.784592I
6.04203 + 4.93414I −1.54489 − 2.49382I
u = 0.563183 − 0.309037I
a = 0.586211 + 0.158353I
b = −0.951603 − 0.784592I
6.04203 − 4.93414I −1.54489 + 2.49382I
u = −0.594374
a = 3.59409
b = 0.575317
2.33297 −12.8660
u = 0.21953 + 1.44872I
a = 0.19440 − 1.71239I
b = 1.007370 + 0.750824I
10.38950 − 7.88778I 3.85457 + 6.32689I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.21953 − 1.44872I
a = 0.19440 + 1.71239I
b = 1.007370 − 0.750824I
10.38950 + 7.88778I 3.85457 − 6.32689I
u = 0.09667 + 1.47937I
a = −0.058612 − 0.469253I
b = −1.152870 + 0.128392I
5.72078 − 1.52942I −2.50362 − 1.38490I
u = 0.09667 − 1.47937I
a = −0.058612 + 0.469253I
b = −1.152870 − 0.128392I
5.72078 + 1.52942I −2.50362 + 1.38490I
u = −0.21415 + 1.48809I
a = −0.663577 − 0.745150I
b = 0.749243 + 0.805642I
11.18290 + 2.01192I 5.40727 − 0.66728I
u = −0.21415 − 1.48809I
a = −0.663577 + 0.745150I
b = 0.749243 − 0.805642I
11.18290 − 2.01192I 5.40727 + 0.66728I
u = −0.14597 + 1.55577I
a = 0.339045 − 1.226810I
b = −0.524487 + 0.125129I
8.32194 + 2.75801I 0.496027 + 0.458149I
u = −0.14597 − 1.55577I
a = 0.339045 + 1.226810I
b = −0.524487 − 0.125129I
8.32194 − 2.75801I 0.496027 − 0.458149I
u = −0.01754 + 1.60857I
a = −0.90265 + 1.90473I
b = 0.903263 − 0.859516I
14.0387 + 3.1794I 4.78161 − 2.41137I
u = −0.01754 − 1.60857I
a = −0.90265 − 1.90473I
b = 0.903263 + 0.859516I
14.0387 − 3.1794I 4.78161 + 2.41137I
u = 0.327398
a = −0.794054
b = 1.08094
0.288303 2.51980
19
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
20
− 8u
19
+ ··· − 15u + 1)(u
94
+ 27u
93
+ ··· + 38u + 1)
c
2
(u
20
− 4u
18
+ ··· + u + 1)(u
94
− u
93
+ ··· − 6u − 1)
c
3
, c
4
(u
20
+ 12u
18
+ ··· + 2u − 1)(u
94
+ u
93
+ ··· + 167u − 29)
c
5
(u
20
− 2u
18
+ ··· − u − 1)(u
94
+ u
93
+ ··· − 48236u − 34973)
c
6
(u
20
− 4u
18
+ ··· − u + 1)(u
94
− u
93
+ ··· − 6u − 1)
c
7
(u
20
+ 8u
19
+ ··· + 15u + 1)(u
94
+ 27u
93
+ ··· + 38u + 1)
c
8
(u
20
− 4u
19
+ ··· + 5u + 1)(u
94
+ u
93
+ ··· + 18u − 1)
c
9
(u
20
+ 12u
18
+ ··· − 2u − 1)(u
94
+ u
93
+ ··· + 167u − 29)
c
10
(u
20
+ 4u
19
+ ··· + 6u + 1)
· (u
94
− 15u
93
+ ··· − 23727557u + 1575181)
c
11
(u
20
+ 4u
19
+ ··· − 5u + 1)(u
94
+ u
93
+ ··· + 18u − 1)
c
12
(u
20
+ u
19
+ ··· + 2u
2
− 1)(u
94
− 4u
93
+ ··· − 1684565u + 327443)
20
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
7
(y
20
+ 16y
19
+ ··· − 19y + 1)(y
94
+ 89y
93
+ ··· + 330y + 1)
c
2
, c
6
(y
20
− 8y
19
+ ··· − 15y + 1)(y
94
− 27y
93
+ ··· − 38y + 1)
c
3
, c
4
, c
9
(y
20
+ 24y
19
+ ··· − 8y + 1)(y
94
+ 105y
93
+ ··· + 13233y + 841)
c
5
(y
20
− 4y
19
+ ··· − 7y + 1)
· (y
94
− 39y
93
+ ··· − 42017779234y + 1223110729)
c
8
, c
11
(y
20
− 24y
19
+ ··· + 39y + 1)(y
94
− 87y
93
+ ··· − 396y + 1)
c
10
(y
20
+ 4y
19
+ ··· − 20y + 1)
· (y
94
+ 49y
93
+ ··· − 1793204056987y + 2481195182761)
c
12
(y
20
− 7y
19
+ ··· − 4y + 1)
· (y
94
− 46y
93
+ ··· − 4312336575555y + 107218918249)
21
